Wednesday, January 16, 2013

"How many dominoes does one need to topple a domino as tall as the Domtoren?"

Supposedly, that was a question in a 2012 Dutch Science Quiz.

Anyone who has followed this blog for any considerable period of time would know that I love reading and studying about mundane phenomena and physics, and this one qualifies as one. PhysicsWorld is reporting a study appearing on ArXiv recently to answer that very question.

The Domtoren is a 112-m-tall cathedral tower in Utrecht and the idea is
to begin with a standard-sized domino, which topples a larger domino.
This then topples an even larger domino and so on until a Domtoren-sized
domino can be felled. The process is called "domino multiplication"
because a tiny tap on the first domino can, in principle, topple a huge
monolith. Now, Van Leeuwen has calculated the upper limit on how much
larger each successive domino can be. In principle, his calculations
suggest that the maximum ratio of successive domino heights can be about
30% larger than the widely accepted value of 1.5.

Of course, he had to make some simplification to his model:

But in the real world not all that energy is channelled into bringing
down the next domino in line. First off, the dominoes bounce a little
as they strike one another. Next, they have a tendency to slip along the
surface they are stood on as they are nudged, lessening the chance of a
fall or causing them to fall back towards the striking domino. And
finally, once in contact, they drag against one another as they fall.

In his model, Van Leeuwen simplifies the situation by assuming that the
collisions are completely inelastic, that the friction between the
dominoes and the surface they stand on is infinite, and that the
dominoes, once touching, experience zero friction and simply slide over
one another.

And of course, there's a video demo, but it isn't related to this particular preprint: